Question: Simplify the following expression: $\dfrac{96z^3}{120z^3}$ You can assume $z \neq 0$.
$ \dfrac{96z^3}{120z^3} = \dfrac{96}{120} \cdot \dfrac{z^3}{z^3} $ To simplify $\frac{96}{120}$ , find the greatest common factor (GCD) of $96$ and $120$ $96 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3$ $120 = 2 \cdot 2 \cdot 2 \cdot 3 \cdot 5$ $ \mbox{GCD}(96, 120) = 2 \cdot 2 \cdot 2 \cdot 3 = 24 $ $ \dfrac{96}{120} \cdot \dfrac{z^3}{z^3} = \dfrac{24 \cdot 4}{24 \cdot 5} \cdot \dfrac{z^3}{z^3} $ $\phantom{ \dfrac{96}{120} \cdot \dfrac{3}{3}} = \dfrac{4}{5} \cdot \dfrac{z^3}{z^3} $ $ \dfrac{z^3}{z^3} = \dfrac{z \cdot z \cdot z}{z \cdot z \cdot z} = 1 $ $ \dfrac{4}{5} \cdot 1 = \dfrac{4}{5} $